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  • View in gallery

    The digital elevation model of peninsular Malaysia showing the study areas: WPM, EPM, and SPM. The mountain range above 2000 m is called Banjaran Titiwangsa, which is the main mountain range that forms the backbone of the peninsular Malaysia. The red markers indicate the data point of OLR with 2.5° × 2.5° spatial resolution.

  • View in gallery

    Precipitation map of annual mean rainfall calculated from TRMM 3B43 (V7) over peninsular Malaysia.

  • View in gallery

    (a) Time series of the daily normalized OLR at WPM from 2003 to 2010 calculated from Eq. (1), where W m−2 and W m−2 are used to compute the wavelet power spectrum. (b) The wavelet plot of daily normalized OLR. The thick solid line is the COI. The dotted contour is confidence level above 95% for a red noise with a lag-1 autocorrelation coefficient of 0.55. The vertical plot on the right contains the GWS of the entire epoch, 2003–10, with 95% confidence level shown as red dotted line. (c) The scale-averaged wavelet power [Eq. (7)] over semiannual and annual bands for the daily OLR data. The thin dashed line and solid line are the 95% confidence levels for semiannual and annual variations, respectively.

  • View in gallery

    As in Fig. 3, but over EPM, with W m−2 and W m−2.

  • View in gallery

    As in Fig. 3, but over SPM, with W m−2 and W m−2.

  • View in gallery

    Comparison of GWS of OLR for WPM, EPM, and SPM from 2003 to 2010.

  • View in gallery

    (a) Time series of the daily normalized OLR at WPM from 2003 to 2010. (b) Real parts of the wavelet coefficients based on daily OLR data from 2003 to 2010 over WPM. (c) The scale average of real parts of wavelet coefficients [Eq. (8)] over semiannual (170–190 days) and annual (350–380 days) bands. The thin dashed line and solid line are the semiannual and annual variations, respectively.

  • View in gallery

    As in Fig. 7, but over EPM.

  • View in gallery

    As in Fig. 7, but over SPM.

  • View in gallery

    (a) Time series of the daily normalized OLR at SPM from 1 Jan 2006 to 31 Dec 2007 calculated from Eq. (1), where W m−2 and W m−2. (b) Phase plot of wavelet coefficients of OLR at SPM from 1 Jan 2006 to 31 Dec 2007.

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Investigating Variability of Outgoing Longwave Radiation over Peninsular Malaysia Using Wavelet Transform

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  • 1 School of Physics, Universiti Sains Malaysia, Penang, Malaysia
  • 2 Institute of Space Science, National Central University, Jhongli, Taiwan
  • 3 School of Physics, Universiti Sains Malaysia, Penang, Malaysia
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Abstract

The present study analyzes and quantifies the spatial–temporal variability of outgoing longwave radiation (OLR) over peninsular Malaysia using the continuous wavelet transform (CWT) from 2003 to 2010. The goal is to understand the long-term variability of OLR over Malaysia in terms of time–frequency variations in relation to the monsoon period and other weather phenomena. The study regions selected were the west coast, east coast, and southern part of peninsular Malaysia. The OLR variation characteristics in time and space derived from wavelet transform were found to be distinctly different in these three regions. In these three regions, OLR showed significant periodicities dominated by the annual cycle, followed by a semiannual cycle. The west coast of peninsular Malaysia has a lower annual component compared to the other regions because of the rain-sheltering effect by the mountain range that blocked the heavy rainfall from northeast monsoon winds. Besides that, the results show that the wet and dry spells coincide with local monsoon and intermonsoon periods. Meanwhile, the results also revealed that the semiannual variation is statistically significant during 2004–06. The strong semiannual variation is coincident with several droughts that resulted from the strong El Niño events in 2004–06. In addition, the phase plot of wavelet coefficients shows that the variations at various scales are in phase, which coincided with the sudden variations of OLR, indicating heavy flood occurrences in the southern part of peninsular Malaysia. The results show that CWT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both time and frequency.

Corresponding author address: C. J. Wong, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia. E-mail: wongcj@usm.my

Abstract

The present study analyzes and quantifies the spatial–temporal variability of outgoing longwave radiation (OLR) over peninsular Malaysia using the continuous wavelet transform (CWT) from 2003 to 2010. The goal is to understand the long-term variability of OLR over Malaysia in terms of time–frequency variations in relation to the monsoon period and other weather phenomena. The study regions selected were the west coast, east coast, and southern part of peninsular Malaysia. The OLR variation characteristics in time and space derived from wavelet transform were found to be distinctly different in these three regions. In these three regions, OLR showed significant periodicities dominated by the annual cycle, followed by a semiannual cycle. The west coast of peninsular Malaysia has a lower annual component compared to the other regions because of the rain-sheltering effect by the mountain range that blocked the heavy rainfall from northeast monsoon winds. Besides that, the results show that the wet and dry spells coincide with local monsoon and intermonsoon periods. Meanwhile, the results also revealed that the semiannual variation is statistically significant during 2004–06. The strong semiannual variation is coincident with several droughts that resulted from the strong El Niño events in 2004–06. In addition, the phase plot of wavelet coefficients shows that the variations at various scales are in phase, which coincided with the sudden variations of OLR, indicating heavy flood occurrences in the southern part of peninsular Malaysia. The results show that CWT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both time and frequency.

Corresponding author address: C. J. Wong, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia. E-mail: wongcj@usm.my

1. Introduction

Multiple time scales are associated with almost all naturally occurring phenomena in the tropical weather and climate system (Weng and Lau 1994). In the tropics, convective activity varies over different time scales ranging from a few hours to a few years. Among the various time scales of tropical convection, diurnal and annual cycles are more prominent. The diurnal cycle of tropical cloudiness may be due to the interaction between the local- and large-scale environmental circulation, and it is found to be more prominent over regions with intense convection (Murakami 1983; Nitta and Sekine 1994). Many studies have demonstrated that outgoing longwave radiation (OLR) is a reasonable indicator of the convective activity over tropical regions (Wang and Xu 1997; Matsumoto and Murakami 2000; Fontaine et al. 2011). For example, it has been used to investigate the relationship between the Madden–Julian oscillation (MJO)-related tropical convection and North American winter surface air temperature (Wheeler and Hendon 2004; Yao et al. 2011). Typically, the highest values of OLR are associated with the warmest areas of the earth’s atmosphere, because they radiate the greatest amounts of longwave radiation to space. The cloud-free equatorial trade wind regions and tropical Pacific are associated with such high OLR values, while the regions of intense convection associated with monsoon appear as regions of low OLR (Chaudhari et al. 2010).

The existence of long-term observations of cloudiness fluctuations over South Asia is seen in the regional distributions of clouds, precipitation, and OLR (Yasunari 1979; Vincent et al. 1998; Chaudhari et al. 2010; Meenu et al. 2010; Boos and Kuang 2010; Romatschke and Houze 2011); however, OLR variability in peninsular Malaysia has not been investigated in the time–frequency space simultaneously. In a previous study, singular spectrum analysis (SSA) on the monthly rainfall data was used to determine the different modes of fluctuations in rainfall over peninsular Malaysia (Moten 1993). Besides that, Wong et al. (2009) used Fourier series to analyze periodic fluctuations of rainfall in peninsular Malaysia. However, the present work uses a new approach to understand the long-term variability of OLR over Malaysia in terms of time–frequency variations by using the wavelet transform in relation to the rainfall. Extreme weather events are also investigated in OLR by using the phase plots from the wavelet transform. Since OLR reflects the quantity of clouds in the atmosphere, convective intensity, and rainfall amount, understanding the spatial and temporal variations of OLR is an important element in gaining knowledge of water balance dynamics on various scales for water resources management and planning.

Traditionally, the Fourier transform (FT) has been used to identify the different frequency components in a data series. However, in this technique of frequency decomposition, one can identify all frequencies present in the data, but it shows no information regarding their temporal locality (Weng and Lau 1994). FT is a useful tool to extract global information of wavelike signals. However, if a signal is altered in a small neighborhood at a certain time instant, the entire spectrum may be affected. Local information is thus split up into a large number of global bases. Nonstationary signals that are altered only in a short time interval may not be detected by Fourier analysis because these signals are averaged out over the whole time domain. The study of nonstationary time series by localizing signals in both frequency and time domains was first introduced by Gabor (1947), using a windowed Fourier transform (WFT) technique. In the WFT technique, the width of the time–frequency window is fixed. The main problem with WFT is the inconsistent treatment of different frequencies: at low frequencies, there are so few oscillations within the window that the frequency localization is lost, while at high frequencies, there are so many oscillations that the time localization is lost. In this regard, wavelet transform is most appropriate because it gives both information of time and frequency simultaneously. By using the wavelet transform on real data, one is able to find out the different frequencies contained in the data as well as the presence of these frequencies at different times. The efficiency of this technique also lies in the fact that the frequency resolution of the power spectrum is not constant. A good frequency resolution is obtained at lower frequencies and a good temporal resolution is obtained at higher frequencies by suitably dilating and compressing the mother wavelet.

In the present study, the wavelet transform is applied to the long-term (8 years) dataset of daily OLR over peninsular Malaysia during 2003–10. As will be seen below, the convective activity over peninsular Malaysia is not uniformly distributed in the time–frequency space, which is, therefore, best studied by wavelet analysis. The data, background of wavelet analysis, and methodology are presented in section 2. In section 3, the results and discussion of variability of OLR in peninsular Malaysia are presented. Finally, the conclusions are presented in section 4.

2. Data and methodology

a. OLR data from NOAA

The daily interpolated OLR data from National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites are used in the present study. OLR data are derived from twice daily (12-h interval) measurements from NOAA polar-orbiting satellites and are described in detail in Gruber and Winston (1978). The grid spacing of the OLR data is 2.5° latitude × 2.5° longitude in units of watts per square meter. The details of the interpolation technique of OLR data are given by Liebmann and Smith (1996). In tropical latitudes, low OLR values correspond to regions of high cloudiness associated with deep convection (Knutson et al. 1986). Regions of OLR values lower than 240 W m−2 are defined as heavy rain areas approximately corresponding to a daily precipitation of about 6 mm (Matsumoto and Murakami 2000). In the present study, regional mean of daily OLR was computed by averaging the four data points for each study region (Fig. 1). To make a comparative study with rainfall from the Tropical Rainfall Measuring Mission (TRMM) satellite, OLR daily data were chosen for the period from January 2003 to December 2010.

Fig. 1.
Fig. 1.

The digital elevation model of peninsular Malaysia showing the study areas: WPM, EPM, and SPM. The mountain range above 2000 m is called Banjaran Titiwangsa, which is the main mountain range that forms the backbone of the peninsular Malaysia. The red markers indicate the data point of OLR with 2.5° × 2.5° spatial resolution.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

b. Rainfall data from TRMM

The present study uses rainfall data from 3B42 daily V006, a blended TRMM rain product, based on TRMM-calibrated multiple-satellite microwave and infrared measurements to show the monsoon rainfall distribution over peninsular Malaysia. The daily accumulated (beginning at 0000 and ending at 2100 UTC; units in millimeters) rainfall product is derived at 3-h intervals with spatial resolution of 0.25° latitude × 0.25° longitude (Huffman et al. 2007). A detailed description of 3B42 daily V006 product can be found online (http://trmm.gsfc.nasa.gov). In the present study, rainfall data from January 2003 to December 2010, for a total of 2922 days, were investigated. Data earlier than 2003 were not considered, as there are significant gaps present that cannot be filled by interpolation (Chang et al. 2005; Liu et al. 2007).

c. Study area

Peninsular Malaysia is divided into east and west coast regions by a mountain range. This mountain range is called Banjaran Titiwangsa, and it is the main mountain range that forms the backbone of peninsular Malaysia (Tan et al. 2011). The climate in Malaysia is hot and humid, with mean temperatures ranging from 25.5° to 33°C. The country experiences rainfall throughout the year, with 150–200 wet days and an annual amount of 2000–4000 mm of rain. To investigate the patterns and variability of OLR in peninsular Malaysia, three regions were selected, that is, the west coast (WPM), east coast (EPM), and southern part (SPM) of peninsular Malaysia, as shown in Fig. 1.

d. Methods

1) Monsoon rainfall contribution

Mean annual accumulated rainfall from 2003 to 2010 was computed over each study region. Southwest monsoon (SWM) and northeast monsoon (NEM) accumulated rainfalls were computed from May to September and from November to March, respectively. Besides that, the total monsoon rainfall (SWM + NEM) was also computed. The results, including the mean values of annual accumulated rainfall, SWM accumulated rainfall, NEM accumulated rainfall, and their contributions (percentage) to annual rainfall, are shown in Table 1. The precipitation map in Fig. 2 shows the annual mean rainfall over peninsular Malaysia from January 2003 to December 2010 by using TRMM 3B43 (V7) monthly rainfall data indicating the spatial variation. It is observed that the east coast of peninsular Malaysia receives maximum rainfall while the west coast receives minimum rainfall.

Table 1.

Summary on the monsoon rainfall contributions over WPM, EPM, and SPM. The percentage shows the rainfall contributions to the annual rainfall.

Table 1.
Fig. 2.
Fig. 2.

Precipitation map of annual mean rainfall calculated from TRMM 3B43 (V7) over peninsular Malaysia.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

2) Normalization of OLR time series

Before applying the wavelet transform, the daily OLR data are normalized by standard deviation using the following equation:
e1
where is the raw data to be standardized, is the mean of the population, is the standard deviation of the population, and z represents the distance between the raw data and the population mean in units of standard deviation. The value z is negative when the raw data is below the mean (wet) and positive when above the mean (dry). This is to facilitate the comparison of results across all regions and years. The daily OLR data were selected from 1 January 2003 to 31 December 2010 for a total series length of 2922 days. The time series of daily normalized OLR over the west coast, east coast, and southern part of peninsular Malaysia are shown in Figs. 3a, 4a, and 5a, respectively.
Fig. 3.
Fig. 3.

(a) Time series of the daily normalized OLR at WPM from 2003 to 2010 calculated from Eq. (1), where W m−2 and W m−2 are used to compute the wavelet power spectrum. (b) The wavelet plot of daily normalized OLR. The thick solid line is the COI. The dotted contour is confidence level above 95% for a red noise with a lag-1 autocorrelation coefficient of 0.55. The vertical plot on the right contains the GWS of the entire epoch, 2003–10, with 95% confidence level shown as red dotted line. (c) The scale-averaged wavelet power [Eq. (7)] over semiannual and annual bands for the daily OLR data. The thin dashed line and solid line are the 95% confidence levels for semiannual and annual variations, respectively.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Fig. 4.
Fig. 4.

As in Fig. 3, but over EPM, with W m−2 and W m−2.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Fig. 5.
Fig. 5.

As in Fig. 3, but over SPM, with W m−2 and W m−2.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

3) Wavelet analysis

A harmonic analysis was performed on the daily OLR by using the continuous wavelet transform (CWT). This is to investigate the dominant periodic variations. The wavelet transform provides an advancement as it is capable of analyzing nonstationary data and gives time–frequency localization (Farge 1992; Torrence and Compo 1998). The wavelet transform, relative to some basic wavelet, provides a flexible time frequency window, which automatically narrows when observing high-frequency components and widens when observing low-frequency components. The technique of using wavelets to identify localized power events in time series is now being used and applied in various geophysical and meteorological studies (e.g., Liu et al. 2005; Das and Sinha 2008; Narasimha and Bhattacharyya 2010). The wavelet analysis in this paper follows the methods of Torrence and Compo (1998). The software was provided by Torrence and Compo (1998) and is available online (http://paos.colorado.edu/research/wavelets/).

For a discrete equally spaced time series , the convolution of with a scaled and translated version of gives the continuous wavelet transform
e2
where N is the number of points in the time series, is the wavelet function (normalized to have unit energy) at scale and translated in time by , is the time step for the analysis, and the asterisk indicates the complex conjugate (Torrence and Compo 1998). By varying the wavelet scale s and translating along the localized time index n, the wavelet coefficients can be computed. The wavelet power spectrum, also called spectrogram, is defined as . In the present study, the wavelet spectrum was calculated for a discrete set of 450 scales. The scales are a series of fractional powers of 2:
e3
where and . The value of should be chosen so that the equivalent Fourier period is approximately (Torrence and Compo 1998). In the present study, is equal to 1 day. This gives scales ranging from 2 to 1024 days. The present study used a Morlet wavelet, which is a plane wave modulated by a Gaussian envelope for computing the wavelet coefficients. It is a complex wavelet and is given as
e4
where is a dimensionless time parameter and is the frequency, here taken to be 6 to satisfy the admissibility condition. The relevant mathematics are described in detail by Farge (1992) and Torrence and Compo (1998).
(i) Significance of wavelet coefficients
The red-noise spectrum Pk was chosen as the background spectrum for testing the significance of the results since the data match this spectrum quite well. A lag-1 autocorrelation coefficient [ in Eq. (5)] of 0.55 was chosen for all three areas of study:
e5
(ii) Cone of influence

The cone of influence (COI) is the demarcation in the wavelet spectrum out of which edge effects become important and is defined as the e-folding time for the autocorrelation of wavelet power at each scale (Torrence and Compo 1998). This e-folding time was chosen as the wavelet power for discontinuity at the edge drops by factor and ensures that the edge effects are negligible beyond this point, that is, within the cone.

(iii) Global wavelet spectrum
Since the wavelet spectrum presents a lot of information in one image, it is often desirable to condense this information by averaging the results over a range of scales or times. One useful technique is to average the power at every scale over the whole time series, to compare the spectral power at different scales. Torrence and Compo (1998) call this a global wavelet spectrum (GWS):
e6
where N is the length of the series .
(iv) Scale-averaged wavelet power
To examine fluctuations in power over a range of scales (a band), one can define the scale-averaged wavelet power as the weighted sum of the wavelet power spectrum over scales from to :
e7
where is a factor for scale averaging, is the time interval, and is the reconstruction factor ( = 0.776 for Morlet). In the present study, the dominant cycles of variation of OLR are at semiannual and annual periods; hence, the scale-averaged wavelet power is computed over these two bands. For semiannual variation, the wavelet power is averaged over 170–190-day band (centered at 180 days), and for annual variation, the wavelet power is averaged over 350–380-day band (centered at 365 days).
(v) Scale-averaged real part of wavelet coefficients
The time-domain signal over the range of scales and can be reconstructed from the wavelet amplitudes via bandpass filtering:
e8
where is the reconstructed (bandpass) signal, is a factor to remove the energy scaling, stands for the real part of the quantity in brackets, and converts the wavelet coefficient to energy density. The wavelet power spectra , the global wavelet spectra, and the corresponding 95% confident levels for the red-noise spectra were determined for each of the time series (west coast, east coast, and southern part of peninsular Malaysia).
(vi) Phase information of wavelet coefficients
Another useful property of the wavelet transform is the phase information:
e9
where and are the imaginary and real parts of the wavelet coefficients, respectively (Torrence and Compo 1998). The phase is given in radians from to . The phase plot of the wavelet coefficients is used to detect singularities or sudden changes by examining the convergence of phase lines in the time–frequency domain (Weng and Lau 1994).

3. Results and discussions

a. Monsoon rainfall contribution over peninsular Malaysia

In general, the rainfall distribution in peninsular Malaysia is governed by monsoon rainfall. Table 1 summarizes the monsoon rainfall contribution in each region. The mean annual rainfall over peninsular Malaysia was approximately 2673, 3173, and 3506 mm at west coast, east coast, and southern region, respectively, during the study period.

For the west coast region, the monsoon rainfalls contribute 88% to the mean annual rainfall, 19.4% and 68.6% of which occurred during the SWM and NEM periods, respectively. The east coast region received a relatively larger amount of mean annual rainfall, 3173 mm, 87.9% of which occurred during the monsoon period. NEM contributes 65.3% to the mean annual rainfall, whereas, SWM contributes a relatively smaller amount of 22.5% to the mean annual rainfall.

For the southern region, the monsoon rainfalls contribute 81.1% to the mean annual rainfall. SWM contributes a relatively smaller amount of 23.5% to the mean annual rainfall. Subsequently, NEM contributes a relatively larger amount of 58.4% to the mean annual rainfall.

Table 1 clearly shows that the mean annual rainfall in each region is mainly dominated by monsoon rainfall, which contributes to over 80% of annual rainfall. The large amount of NEM rainfall clearly stands out from peninsular Malaysia as a whole. During NEM, the wind speed may attain values higher than 55.56 km h−1 (30 kt), which is much greater than the wind speed of 27.78 km h−1 (15 kt) during SWM (Nieuwolt 1968; Suhaila and Jemain 2008). According to Back and Bretherton (2005), higher wind speeds promote more evaporation, which destabilizes the boundary layer and can trigger deep convection and, hence, increase precipitation. On the other hand, the period of SWM is a drier period for the whole peninsular Malaysia, particularly for the states of the west coast (Suhaila and Jemain 2008). In addition, the west coast region recorded the lowest NEM rainfall amount. This probably occurred because the northeasterly winds during NEM are blocked by the Main Range (Banjaran Titiwangsa), where the high mountain ranges create rain sheltering effects for the west coast region (Suhaila and Jemain 2008). Also, Camerlengo et al. (1998) stated that the humidity of the air mass moving further inland is greater on the east coast than on the west coast. Figure 2 clearly shows that east coast has higher rainfall compared to that of the west coast.

b. Wavelet analysis of OLR

Figures 3a, 4a, and 5a are the time series of the normalized daily OLR data over the west coast, east coast, and southern part of peninsular Malaysia, respectively, and were used to compute the wavelet power spectrum. Positive values indicate that the OLR is above the mean value, in other words a dry spell, and negative OLR means a wet spell. Figures 3b, 4b, and 5b are the wavelet spectrograms of the data at the west coast, east coast, and southern part of peninsular Malaysia, respectively, with the color bar on the left. Since the data series were mean centered and normalized, the spectral power is dimensionless. Therefore, the wavelet power expresses the variance of the series as squared standard deviations from the mean. The thick solid line is the COI of the spectrogram. Wavelet coefficients outside this cone are subject to edge effects and are not completely reliable. Wavelet power with a confidence level of 95% is shown by the dotted contour. The vertical plot on the right is the GWS obtained by averaging the wavelet power over the entire time duration, that is, during 2003–10. The dotted red lines show 95% confidence level. The intensity of semiannual, annual, and quasi-biennial components during different epochs can be seen clearly in the spectrograms. One can see in these plots that the contribution of the annual component is statistically significant and present throughout the period of study over all regions. On the other hand, the semiannual variation is also present over all three regions but is statistically significant only during 2004–06. Figures 3c, 4c, and 5c present the scale-averaged wavelet power of OLR for the west coast, east coast, and southern part of peninsular Malaysia, respectively, in the semiannual and annual bands during 2003–10. The thin dashed line and the solid line are the 95% confidence level for semiannual and annual components, respectively. As seen in the spectrograms, the average power of the semiannual component during 2004–06 is high and statistically significant for all three regions. On the other hand, the average power of the annual component is statistically significant during the whole period from 2003–10; however, it varies with time and is moderately different for the three regions.

c. Annual and semiannual variability of OLR

The annual variation is represented by a rather evenly warm colored horizontal contour at the period of 365 days (Figs. 3b, 4b, 5b). The annual variation is the predominant feature for the west coast, east coast, and southern part of peninsular Malaysia. This is because the precipitation in peninsular Malaysia is dominated by NEM (Camerlengo and Demmler 1997; Tangang 2001; Suhaila and Jemain 2009; Wong et al. 2009; Varikoden et al. 2010). The accumulated rainfall from NEM contributes over 60% to the annual rainfall (see Table 1). Besides that, there is also significant power at semiannual variation (180 days) from 2004 to 2006 in these three regions, with the highest power occurring at 2005–06 (Figs. 3c, 4c, 5c). It is interesting to note that this period coincides with several droughts that resulted from the strong El Niño events during 2004–06 (Daud et al. 2010). These droughts probably played a role in the semiannual variation of OLR during 2004–06, although they did not follow a semiannual variation over Malaysia. Several studies suggested that peninsular Malaysia experienced anomalously low rainfall during the El Niño year (e.g., Tangang 2001; Tangang and Juneng 2004). In physical terms, OLR is strongly controlled by the presence of water vapor in atmosphere and the presence of clouds (Paynter and Ramaswamy 2012). During drought, there is less water vapor in the atmosphere, and hence, the OLR is high (Huang and Ramaswamy 2009). Furthermore, drought might cause biomass burning and load the atmosphere with anthropogenic aerosols (Field et al. 2009; Tangang 2010). Those smoke particles are observed to be coming from southern Thailand and Sumatra to over Malaysia (Liew et al. 2009; Reid et al. 2013) and might affect the OLR by reducing the amount of solar radiation received at the surface (Ackerman et al. 2000; Lin et al. 2006; Tangang 2010). Hence, it is envisaged that there is probably more than one source to the semiannual variation of OLR. Further in-depth analyses are required to understand the temporal variation of the semiannual amplitude and the contribution of different factors to the same.

Figure 6 is the comparison of the GWS of OLR for west coast, east coast, and southern part of peninsular Malaysia from 2003 to 2010. The power around the 365-day period is the dominant feature in all the global spectra, indicating strong annual variation in the time series. The results show that semiannual variation is comparable in magnitude to annual variation over the west coast of peninsular Malaysia. Previous studies have shown that semiannual variation tends to be concentrated over the western part of peninsular Malaysia, which is the transitional zone between summer and winter monsoon (e.g., Chang 2004; Chang et al. 2005). Besides that, Fig. 6 clearly shows that WPM has a lower annual component compared to the other two regions. This could be due to the fact that the west coast of peninsular Malaysia that is exposed to the SWM tends to be drier than the east coast of peninsular Malaysia that is exposed to the NEM (Suhaila and Jemain 2008), whereas over the east coast and southern regions, annual power is significantly higher compared to semiannual power because of the domination of NEM. These results are consistent with the harmonic analysis of monthly rainfall in peninsular Malaysia by Wong et al. (2009), where the dominant periodic fluctuation is the annual variation and the second most important fluctuation is at a half-year period in east coast region. One of the new findings of this work is that the annual variation in the southern region is slightly higher than the west and east coasts during 2003–10 (Fig. 6).

Fig. 6.
Fig. 6.

Comparison of GWS of OLR for WPM, EPM, and SPM from 2003 to 2010.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Figures 7b, 8b, and 9b present the real part of wavelet coefficients in the time–frequency domain for the daily OLR data from 1 January 2003 to 31 December 2010, shown in Figs. 7a, 8a, and 9a, for the different regions of study. The negative intensities imply wet spells, and the positive intensities imply dry spells. Figures 7c, 8c, and 9c show the scale averages of the real part of the wavelet coefficients over semiannual and annual bands at the west coast, east coast, and southern part of peninsular Malaysia, respectively. The positive peak values of the sinusoidal curves in Figs. 7c, 8c, and 9c indicate the dry spells, whereas the negative peak values indicate the wet spells. The averages of wavelet coefficients for semiannual and annual components vary with time and are different for the three regions. The summaries of the semiannual and annual variations of OLR for the three regions are presented in Table 2. For the west coast of peninsular Malaysia, the annual dry spell occurs during the end of March to the beginning of April, which coincides with the end of NEM and the intermonsoon period. During the intermonsoon period, of which April is the most typical month, wind velocities are low, wind directions are highly variable, and there is often no clear general circulation at all (Nieuwolt 1968). The annual wet spell occurs during September–October. As October is a transitional month between monsoons, before the beginning of NEM, the wet spell may be solely attributed to the southward motion of the ITCZ (Camerlengo et al. 1998). For the east coast of peninsular Malaysia, the annual dry spell occurs during April–May, which coincides with the intermonsoon and the beginning of the SWM. It is well known that the eastern region in peninsular Malaysia is more prone to experience dry spells during April (Daud et al. 2010; Varikoden et al. 2010). Besides that, the annual wet spell occurs during October–November, which coincides with the beginning of the NEM period. It is well known that rainfall in the east coast region of peninsular Malaysia is mostly influenced by the NEM (Camerlengo and Demmler 1997; Tangang 2001; Suhaila and Jemain 2009; Varikoden et al. 2010). In the southern part of peninsular Malaysia, the annual dry spell occurs during May–June, whereas the annual wet spell occurs during November–January, which coincides with the NEM period. Besides annual variation, there are semiannual components in these three regions. The positive phase of semiannual variation occurred in February–March and August, whereas, negative phase of semiannual variation occurred in May and November over these three regions. These results are consistent with Wang and Ding (2008), who extracted major modes of seasonal variation in the tropics using multivariable empirical orthogonal function analysis of the 12-month climatology.

Fig. 7.
Fig. 7.

(a) Time series of the daily normalized OLR at WPM from 2003 to 2010. (b) Real parts of the wavelet coefficients based on daily OLR data from 2003 to 2010 over WPM. (c) The scale average of real parts of wavelet coefficients [Eq. (8)] over semiannual (170–190 days) and annual (350–380 days) bands. The thin dashed line and solid line are the semiannual and annual variations, respectively.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Fig. 8.
Fig. 8.

As in Fig. 7, but over EPM.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Fig. 9.
Fig. 9.

As in Fig. 7, but over SPM.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

Table 2.

Comparison of semiannual and annual variations of OLR over west coast, east coast, and southern part of peninsular Malaysia.

Table 2.

d. Phase plot of wavelet coefficients

The phase plot of the wavelet coefficients was used to detect the singularities or the sudden changes by examining the convergence of the phase line in the time–frequency domain (Weng and Lau 1994). In 2006–07, there were a few extreme flood events that happened in the southern part of peninsular Malaysia (Tangang et al. 2008). The phase plot was used to figure out those flood events in the present study. Figure 10b is the phase plot of the wavelet coefficients at the southern part of peninsular Malaysia for 2006–07. The local phase is given by shading density on the plot. At each scale, from left to right within a cycle, one can follow an increase in brightness, corresponding to a increase of the phase from to . When the phase reaches to , it is wrapped around to the value of . The distinct division between and clearly shows constant phase line for each cycle at each scale. Several locations of convergence of constant phase lines (the same phase occurring over a wide range of scales) are seen in this plot, corresponding to sudden variations in the time series (Weng and Lau 1994). For example, there are two significant convergences of constant phase lines occurring from December 2006 to January 2007 and July 2007. The December 2006/January 2007 flood was the worst flood disaster in the southern part of peninsular Malaysia (Johor Bahru) in 100 years caused by extreme precipitation events (Tangang et al. 2008). These extreme precipitation events were mainly due to strong northeasterly winds over the South China Sea that interacted with the large-scale circulation associated with the MJO, which caused low-level convergence and enhanced deep convection over the southern part of peninsular Malaysia and, hence, caused the flood (Tangang et al. 2008). This deep convection is indicated by the very low OLR during this period.

Fig. 10.
Fig. 10.

(a) Time series of the daily normalized OLR at SPM from 1 Jan 2006 to 31 Dec 2007 calculated from Eq. (1), where W m−2 and W m−2. (b) Phase plot of wavelet coefficients of OLR at SPM from 1 Jan 2006 to 31 Dec 2007.

Citation: Journal of Climate 26, 10; 10.1175/JCLI-D-12-00345.1

4. Summary

Wavelet transform is an effective tool to quantify and compare the multiscale variability of daily OLR over peninsular Malaysia. Evidence has been presented that OLR data from NOAA are adequate, at least within the scope of the present study, to delineate some of the characteristic features of the monsoon in peninsular Malaysia. Three distinct regions, namely, the west coast, east coast, and southern part of peninsular Malaysia, were selected for the analysis. This study presents the following conclusions:

  1. Monsoon rainfall contributes over 80% of the mean annual rainfall over study regions. The large amount of NEM rainfall clearly stands out from peninsular Malaysia as a whole because of stronger wind speed during NEM.
  2. Wavelet analysis of variability of OLR shows annual and semiannual variations as the dominant features in the west coast, east coast, and southern part of peninsular Malaysia. These variations are characterized by the monsoon and intermonsoon periods. The wet spells coincide with the NEM period and southward motion of the ITCZ and the dry spells coincide with intermonsoon period.
  3. The west coast of peninsular Malaysia has a lower annual component compared to the east coast of peninsular Malaysia because the heavy rainfall from NEM is blocked by the mountain range. On the other hand, the semiannual variation over the west coast is comparable in magnitude to the annual variation because it is located at the transitional zone between summer and winter monsoon.
  4. There is strong semiannual variation during 2004–06 over the three study regions, which is coincident with several droughts that resulted from the strong El Niño events during the period. Those droughts may have probably played a role in the semiannual variation of OLR during 2004–06, although they did not follow a semiannual variation over Malaysia. However, this is not the entire explanation; further investigations are required to completely understand the variation.
  5. Another new finding from the present work is that the GWS shows a slightly higher annual variation over the southern region compared to the west coast and east coast during 2003–10. This has not been reported in earlier studies.
  6. The locations of convergence of phase lines corresponding to sudden changes in OLR indicate flood events. The sudden change of OLR is due to the strong northeasterly winds over the South China Sea that interacted with the large-scale circulation associated with the MJO, which caused low-level convergence and enhanced deep convection and consequent precipitation over the southern part of peninsular Malaysia.

It can be concluded that OLR is a good parameter to understand the monsoon variation over peninsular Malaysia. The wavelet spectrogram of OLR revealed its variability in time and frequency space while simultaneously indicating monsoonal changes in peninsular Malaysia. Further analysis with respect to measured rainfall, cloud coverage, and other meteorological parameters would enhance this understanding and would be taken up at a later stage.

Acknowledgments

The authors gratefully acknowledge Mr. S. S. Yang from the Institute of Space Science, National Central University, Taiwan, for providing helpful advice. The authors also acknowledge Mr. Tan Fuyi from the School of Physics, Universiti Sains Malaysia, for providing the digital elevation model of peninsular Malaysia. The OLR data used in the paper were provided by the National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites. The precipitation data used in the paper were provided by the Tropical Rainfall Measuring Mission (TRMM). This research is supported by the Universiti Sains Malaysia under Research University Fund (1001/JPNP/AUPK002), a short-term grant (304/PFIZIK/6310057), a postgraduate incentive grant (1001/PFIZIK/822074), and a Research University (RU) grant (PFIZIK/1001/814078) and by NSC of Taiwan through Grant NSC 101-2111-M008-011.

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